My intuition is that "a fan of Rihanna" is taken to mean 'a fan of Rihanna's music'. What do you think of the following?

(15) Rihanna is my friend, and a wonderful and caring person. I guess you could say I'm a fan of Rihanna's

Does it get better when it's clear you aren't only talking about her output, but rather her as a person? If the music is what's intended, then maybe #fan of Rihanna's in (2) is due to it being more like the coffee example.